We study the dependence of the electrical conductivity on the gold concentration of Au-implanted polymethylmethacrylate (PMMA) and alumina nanocomposite thin films. For Au contents larger than a critical concentration, the conductivity of Au-PMMA and Au-alumina is well described by percolation in two dimensions, indicating that the critical correlation length for percolation is larger than the thickness of the films. Below the critical loading, the conductivity is dominated by tunneling processes between isolated Au particles dispersed in PMMA or alumina continuous matrices. Using an effective medium analysis of the tunneling conductivity, we show that Au-PMMA behaves as a tunneling system in two dimensions, as the film thickness is comparable to the mean Au particle size. On the contrary, the conductivity of Au-alumina films is best described by tunneling in three dimensions, although the film thickness is only a few times larger than the particle size. We interpret the enhancement of the effective dimensionality of Au-alumina films in the tunneling regime as due to the larger film thickness as compared to the mean interparticle distances.
References
We approximate the typical inter-particle distance δ by the mean distance between nearest neighboring particles. For a system of randomly distributed particles of number density ρ, there is in average one particle contained within a volume centered about a given particle: , so that .
It is possible to estimate the values of x below which Au-alumina films behave as 2d percolating systems by using , where ν ≈ 0.88 is the 3d correlation length exponent. Using xc ≃ 0.44 and h ≈ 6D, we obtain that ζ becomes greater than the film thickness when the Au concentration is lower than about 0.65.
